Abstract

High spectral resolution lidars (HSRLs) have shown great value in aircraft aerosol remote sensing application and are planned for future satellite missions. A compact, robust, quasi-monolithic tilted field-widened Michelson interferometer is being developed as the spectral discrimination filter for an second-generation HSRL(HSRL-2) at NASA Langley Research Center. The Michelson interferometer consists of a cubic beam splitter, a solid arm and an air arm. Piezo stacks connect the air arm mirror to the body of the interferometer and can tune the interferometer within a small range. The whole interferometer is tilted so that the standard Michelson output and the reflected complementary output can both be obtained. In this paper, the transmission ratio is proposed to evaluate the performance of the spectral filter for HSRL. The transmission ratios over different types of system imperfections, such as cumulative wavefront error, locking error, reflectance of the beam splitter and anti-reflection coatings, system tilt, and depolarization angle are analyzed. The requirements of each imperfection for good interferometer performance are obtained.

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References

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  1. C. Weitkamp and E. Eloranta, “High Spectral Resolution Lidar,” in Lidar (Springer Berlin / Heidelberg, 2005), pp. 143–163.
  2. S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, and J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation,” Appl. Opt. 22(23), 3716–3724 (1983).
    [CrossRef] [PubMed]
  3. M. Esselborn, M. Wirth, A. Fix, M. Tesche, and G. Ehret, “Airborne high spectral resolution lidar for measuring aerosol extinction and backscatter coefficients,” Appl. Opt. 47(3), 346–358 (2008).
    [CrossRef] [PubMed]
  4. J. W. Hair, C. A. Hostetler, A. L. Cook, D. B. Harper, R. A. Ferrare, T. L. Mack, W. Welch, L. R. Izquierdo, and F. E. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47(36), 6734–6752 (2008).
    [CrossRef] [PubMed]
  5. D. Bruneau and J. Pelon, “Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a Mach-Zehnder interferometer: principle of operation and performance assessment,” Appl. Opt. 42(6), 1101–1114 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2008 (2)

2003 (1)

2001 (2)

1997 (1)

M. J. McGill and W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36(1), 139–145 (1997).
[CrossRef]

1994 (1)

1990 (1)

1985 (2)

1983 (2)

1979 (1)

1972 (1)

Ansmann, A.

Bruneau, D.

Caldwell, L. M.

Cook, A. L.

Ehret, G.

Eloranta, E. W.

Esselborn, M.

Ferrare, R. A.

Fix, A.

Gault, W. A.

Hair, J. W.

Harper, D. B.

Haslett, J. W.

Hostetler, C. A.

Hovis, F. E.

Izquierdo, L. R.

Johnston, S. F.

Kendall, D. J. W.

Kosteniuk, P. R.

Krueger, D. A.

Mack, T. L.

McCormick, M. P.

McGill, M. J.

M. J. McGill and W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36(1), 139–145 (1997).
[CrossRef]

Miller, D. W.

Pasturczyk, Z.

Pelon, J.

Piironen, P.

Riebesell, M.

Ring, J.

Roesler, F. L.

Russell, P. B.

Schofield, J. W.

She, C.-Y.

Shepherd, G. G.

Shipley, S. T.

Skinner, W. R.

M. J. McGill and W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36(1), 139–145 (1997).
[CrossRef]

Sroga, J. T.

Swissler, T. J.

Tesche, M.

Tracy, D. H.

Trauger, J. T.

Weinman, J. A.

Weitkamp, C.

Welch, W.

Wimperis, J. R.

Wirth, M.

Appl. Opt. (11)

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, and J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation,” Appl. Opt. 22(23), 3716–3724 (1983).
[CrossRef] [PubMed]

M. Esselborn, M. Wirth, A. Fix, M. Tesche, and G. Ehret, “Airborne high spectral resolution lidar for measuring aerosol extinction and backscatter coefficients,” Appl. Opt. 47(3), 346–358 (2008).
[CrossRef] [PubMed]

J. W. Hair, C. A. Hostetler, A. L. Cook, D. B. Harper, R. A. Ferrare, T. L. Mack, W. Welch, L. R. Izquierdo, and F. E. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47(36), 6734–6752 (2008).
[CrossRef] [PubMed]

D. Bruneau and J. Pelon, “Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a Mach-Zehnder interferometer: principle of operation and performance assessment,” Appl. Opt. 42(6), 1101–1114 (2003).
[CrossRef] [PubMed]

C.-Y. She, “Spectral structure of laser light scattering revisited: bandwidths of nonresonant scattering lidars,” Appl. Opt. 40(27), 4875–4884 (2001).
[CrossRef] [PubMed]

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, and J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation,” Appl. Opt. 22(23), 3716–3724 (1983).
[CrossRef] [PubMed]

P. B. Russell, T. J. Swissler, and M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18(22), 3783–3797 (1979).
[PubMed]

J. W. Hair, L. M. Caldwell, D. A. Krueger, and C.-Y. She, “High-spectral-resolution lidar with iodine-vapor filters: measurement of atmospheric-state and aerosol profiles,” Appl. Opt. 40(30), 5280–5294 (2001).
[CrossRef] [PubMed]

J. Ring and J. W. Schofield, “Field-compensated michelson spectrometers,” Appl. Opt. 11(3), 507–516 (1972).
[CrossRef] [PubMed]

G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII: wide-angle Michelson Doppler imaging interferometer for Spacelab,” Appl. Opt. 24(11), 1571–1584 (1985).
[CrossRef] [PubMed]

W. A. Gault, S. F. Johnston, and D. J. W. Kendall, “Optimization of a field-widened Michelson interferometer,” Appl. Opt. 24(11), 1604–1608 (1985).
[CrossRef] [PubMed]

Opt. Eng. (1)

M. J. McGill and W. R. Skinner, “Multiple Fabry-Perot interferometers in an incoherent Doppler lidar,” Opt. Eng. 36(1), 139–145 (1997).
[CrossRef]

Opt. Lett. (2)

Other (6)

C. Weitkamp and E. Eloranta, “High Spectral Resolution Lidar,” in Lidar (Springer Berlin / Heidelberg, 2005), pp. 143–163.

A. Heliere, A. Lefebvre, T. Wehr, J.-L. Bezy, and Y. Durand, “The EarthCARE mission: Mission concept and lidar instrument pre-development,” in the 23rd International Laser Radar Conference (IEEE International, Nara, Japan, 2006).

D. Malacara, Optical Shop Testing (John Wiley & Sons, Inc., New Jersey, 2007).

P. Hariharan, Optical Interferometry (Academic Press, 2003).

“Matlab Peaks Function,” (The Mathworks), http://www.mathworks.com/help/techdoc/ref/peaks.html .

http://www.lightmachinery.com/Fluid-Jet-Polishing.html .

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram for an HSRL return spectra, (a) is the input backscatter signal in HSRL, and (b) is a set of possible output signal in the molecular backscatter channel.

Fig. 2
Fig. 2

Ray diagram of Michelson interferometer.

Fig. 3
Fig. 3

Comparison of OPD incident angle dependence between ordinary and field-widened Michelson interferometers, (a) incident angle dependence comparison, (b) detailed illustration of the performance of the field-widened MI.

Fig. 4
Fig. 4

Spectral discrimination schematic diagram of a field-widened Michelson spectral filter in HSRL system.

Fig. 5
Fig. 5

Layout of the field-widened Michelson spectral filter.

Fig. 6
Fig. 6

Field-widened performance of the Michelson interferometer.

Fig. 7
Fig. 7

Different cumulative wavefront error distributions, (a) tilt, (b) defocus, (c) random distribution.

Fig. 8
Fig. 8

System responses over RMS value of wavefront, (a) aerosol transmission ratio, (b) molecular transmission ratio change.

Fig. 9
Fig. 9

System responses over locking error, (a) aerosol transmission ratio, (b) molecular transmission ratio change.

Fig. 10
Fig. 10

System responses over tilt angle, (a) aerosol transmission ratio, (b) molecular transmission ratio change.

Fig. 11
Fig. 11

System responses over reflectance of 50/50 beam splitter, (a) is aerosol transmission ratio, and (b) is molecular transmission ratio change. Two curves are shown on each plot corresponding to different assignment of the “aerosol channel”.

Fig. 12
Fig. 12

System responses over reflectance of AR coating, and (a) is aerosol transmission ratio, and (b) molecular transmission ratio change.

Fig. 13
Fig. 13

System responses over polarization angle, and (a) is aerosol transmission ratio, and (b) molecular transmission ratio change.

Equations (19)

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T I =2 I 0 t 0 r 0 [1+cos2πW]
T II = I 0 { t 0 2 + r 0 2 +2 t 0 r 0 cos[2πW+2( δ T + δ R )]} = I 0 ( t 0 2 + r 0 2 ){1+ 2 t 0 r 0 t 0 2 + r 0 2 cos[2πW+2( δ T + δ R )]} ,
T I '= 2I(ν) t 0 (ν) r 0 (ν)[1+cos2πW(ν)] dν
T II '= I(ν){ t 0 2 (ν)+ r 0 2 (ν)+2 t 0 (ν) r 0 (ν)cos[2πW(ν)+2( δ T (ν)+ δ R (ν))]} dν,
W=2 n 1 d 1 cos θ 1 2 n 2 d 2 cos θ 2 ,
{ n 0 sin θ 0 = n 1 sin θ 1 n 0 sin θ 0 = n 2 sin θ 2 .
W=2[ n 1 d 1 (1 sin 2 θ 0 n 1 2 ) 1/2 n 2 d 2 (1 sin 2 θ 0 n 2 2 ) 1/2 ].
W=2( n 1 d 1 n 2 d 2 ) sin 2 θ 0 ( d 1 n 1 d 2 n 2 ) sin 4 θ 0 4 ( d 1 n 1 3 d 2 n 2 3 ) sin 6 θ 0 8 ( d 1 n 1 5 d 2 n 2 5 ) ,
d 1 / n 1 d 2 / n 2 =0.
W=2( n 1 d 1 n 2 d 2 ) sin 4 θ 0 4 ( d 1 n 1 3 d 2 n 2 3 ) sin 6 θ 0 8 ( d 1 n 1 5 d 2 n 2 5 )
T mM = S m (v)* T M (v)dv,
T mA = S m (v)* T A (v)dv,
T aM = S a (v)* T M (v)dv,
T aA = S a (v)* T A (v)dv,
a = T aA T aM ,
m = T mA T mM .
Δ m = MTRMT R 0 MT R 0 ×100%,
T I '= I Coht,I + I bkgd,I
T II '= I Coht,II + I bkgd,II ,

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